To find the product of the polynomials \( (2q^9 + 3q^7)(-6q^2 + 9) \), we need to use the distributive property (also known as the FOIL method for binomials).
Let's break it down step by step:
-
Multiply \( 2q^9 \) by each term in \( -6q^2 + 9 \):
- \( 2q^9 \cdot (-6q^2) = -12q^{11} \)
- \( 2q^9 \cdot 9 = 18q^9 \)
-
Multiply \( 3q^7 \) by each term in \( -6q^2 + 9 \):
- \( 3q^7 \cdot (-6q^2) = -18q^9 \)
- \( 3q^7 \cdot 9 = 27q^7 \)
Now we can combine all these results together:
\[ -12q^{11} + 18q^9 - 18q^9 + 27q^7 \]
Next, combine like terms:
- The \( q^9 \) terms:
- \( 18q^9 - 18q^9 = 0 \)
So we are left with:
\[ -12q^{11} + 27q^7 \]
Thus, the final product is
\[ -12q^{11} + 27q^7 \]
This corresponds to the response:
−12q11+27q7 (negative 12 q to the 11th power plus 27 q to the 7th power).
1 answer